曹禮群+黃記祖

摘 要：構(gòu)一體化的熱、力耦合多尺度模型與算法研究是力學(xué)、數(shù)學(xué)、物理學(xué)與材料科學(xué)多學(xué)科交叉的前沿領(lǐng)域，也是重大裝備研發(fā)中需要著重解決的基礎(chǔ)科學(xué)問題。材料與結(jié)構(gòu)在裂紋、空洞、夾雜、纖維取向、基體分布形態(tài)等方面具有內(nèi)在的不確定性，其損傷和破壞還表現(xiàn)為復(fù)雜的熱力耦合非線性多尺度力學(xué)行為。尺度間隙和跨尺度連接，涉及微—細(xì)—宏觀不同尺度間數(shù)學(xué)物理模型的聯(lián)系與差別等基本問題，建立微/納米尺度的熱、力模型，揭示熱、力耦合的物理機(jī)制，發(fā)展材料與結(jié)構(gòu)一體化的宏—細(xì)—微觀耦合的多尺度模型與算法，具有重要的理論與實(shí)際意義。結(jié)果表明：復(fù)合材料界面結(jié)構(gòu)對于材料的力、熱、電、磁等物理、力學(xué)性能有十分重要的影響。我們針對復(fù)合材料與界面納米結(jié)構(gòu)熱傳導(dǎo)問題，發(fā)展了一類分子動力學(xué)與連續(xù)模型跨尺度耦合模式、MD/FEM耦合算法，并編寫了相關(guān)計(jì)算程序。主要進(jìn)展有：（1）實(shí)現(xiàn)了納米結(jié)構(gòu)導(dǎo)熱系數(shù)等熱學(xué)參數(shù)的分子動力學(xué)計(jì)算和量子校正；（2）發(fā)展了復(fù)合材料和多孔材料周期及隨機(jī)結(jié)構(gòu)熱傳導(dǎo)問題連續(xù)模型的多尺度算法；（3）提出了一類分子動力學(xué)與連續(xù)模型的跨尺度關(guān)聯(lián)模式和MD/FEM耦合算法；（4）實(shí)現(xiàn)了三維復(fù)合材料和界面納米結(jié)構(gòu)的MD/FEM計(jì)算。

關(guān)鍵詞：分子動力學(xué)-連續(xù)介質(zhì)耦合模型 熱傳導(dǎo) 多尺度漸近展開 分子動力學(xué) 有限元方法

A Molecular Dynamics-Continuum Coupled Model for Heat Transfer in Composite Materials

Cao Liqun1 Huang Jizu2

（1.Academy of Mathematics and Systems Science； 2.Institute of Software Chinese Academy of Sciences）

Abstract：The heat transfer problem in composite materials has been investigated which contain the nano-scale interface. A molecular dynamics-continuum coupled model is developed to study the heat transport from the macro- to the micro-scales. The model includes four major steps：（1）A reverse non-equilibrium molecular dynamics （RNEMD） is used to calculate some physical parameters such as the thermal conductivities on the interface.（2）The homogenization method is applied to compute the homogenized thermal conductivities of composite materials.（3）the temperature field in the global structure of composite materials is computed with the multiscale asymptotic method for the macroscopic heat transfer equation.（4）A molecular dynamics-continuum coupled model has been developed to reevaluate the temperature field of composite materials， in particular， the local temperature field near the interface. The numerical results in one-， two- and three-dimensional structures of composite materials including the nano-scale interface are given. Good agreement has been achieved between the numerical results of the proposed coupled algorithm and those of the full MD simulation， demonstrating the accuracy of the present method and its potential applications in the thermal engineering of composite materials.

Key Words：A molecular dynamics-continuum coupled model； Heat transfer； Multiscale asymptotic expansion； Molecular dynamics； Finite element method

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